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The three planes 4y+6z=5,2x+3y+5z=5a n d...

The three planes `4y+6z=5,2x+3y+5z=5a n d6x+5y+9z=10` a. `` meet in a point b. have a line in common c. form a triangular prism d. none of these

A

meet in a point

B

have a line in common

C

form a triangular prism

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
Plane pasing through the line of intersection of planes `4y+6z= 5 and 2x+3y + 5z= 5 ` is
`" "(4y+6z-5)+ lamda(2x+3y+5z-5)=0`
or `" "2lamdax+(3lamda+4)y + (5lamda+6)z- 5lamda-5=0`
Clearly, for `lamda= -3`, we get the plane `6x+5y+9z=10 `.
Hence, the given three planes have common line of intersection.
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